This paper is concerned with cross-sectional dependence arising because observations are interconnected through an observed network. Following Doukhan and Louhichi (1999), we measure the strength of dependence by covariances of nonlinearly transformed variables. We provide a law of large numbers and central limit theorem for network dependent variables. We also provide a method of calculating standard errors robust to general forms of network dependence. For that purpose, we rely on a network heteroskedasticity and autocorrelation consistent (HAC) variance estimator, and show its consistency. The results rely on conditions characterized by tradeoffs between the rate of decay of dependence across a network and network's denseness. Our approach can accommodate data generated by network formation models, random fields on graphs, conditional dependency graphs, and large functional-causal systems of equations.
翻译:本文涉及跨部门依赖性,因为观测通过观测的网络相互连接。在Doukhan和Louhichi(1999年)之后,我们通过非线性变异变量的共变变量来衡量依赖性强度。我们为网络依赖变量提供了大量数字和中心限制理论的法则。我们还提供了一种方法,用以计算对网络依赖性的一般形式具有强力的标准错误。为此,我们依靠一个网络传导和自动调节差异估计器(HAC),并显示其一致性。结果取决于网络依赖性衰减速度与网络密度之间的权衡。我们的方法可以容纳网络形成模型、图表上的随机字段、有条件依赖性图表以及大型功能-视像等式系统生成的数据。